2017, Rapporto tecnico, ENG
NOCERA, L.
We argue that the electrostatic field profile observed by ARTEMIS in the neighbourhood of the lunar surface is sustained by singular electron an ion velocity distribution functions. These are singular solutions of the steady state, two species Vlasov-Poisson equations. The energy distributions of the hot, finite mass, mobile ions is assumed to be log singular at the position of the electric potential's minimum. We show that the electron energy distributions on opposite sides of this minimum are not equal. This leads to a jump discontinuity of the electron distribution across its separatrix. A simple relation exists between the difference of these two electron distributions and that of the ions. The distributions of both species are given in terms of elementary functions and they meet smooth boundary conditions at one plasma end. Simple, finite amplitude profiles of the electric potential result from Poisson equation, which are smoothly, but non monotonically and non symmetrically distributed in space. Three such solutions are investigated in detail as appropriate for non monotonic double layers and for a plasma of semi-infinite extent bounded by a surface.
2015, Articolo in rivista, ENG
Luigi Nocera, Laura J Palumbo
We present new elementary, exact weak singular solutions of the steady state, two species, electrostatic, one dimensional Vlasov-Poisson equations. The distribution of the hot, finite mass, mobile ions is assumed to be log singular at the position of the electric potential's minimum. We show that the electron energy distributions on opposite sides of this minimum are not equal. This leads to a jump discontinuity of the electron distribution across its separatrix. A simple relation exists between the difference of these two electron distributions and that of the ions. The velocity Fourier transform of the electron singular distribution is smooth and appears as a simple Neumann series. Elementary, finite amplitude profiles of the electric potential result from Poisson equation, which are smoothly, but nonmonotonically and asymmetrically distributed in space. Two such profiles are given explicitly as appropriate for a nonmonotonic double layer and for a plasma bounded by a surface. The distributions of both electrons and ions supporting such potential meet smooth and kinetically stable boundary conditions at one plasma boundary. For sufficiently small potential to electron temperature ratios, the nonthermal, discontinuous electron distribution resulting at the other plasma boundary is also stable against Landau damped perturbations of the electron distribution.
2013, Rapporto tecnico, ENG
Nocera L; Palumbo LJ
We present exact, weak, two species Vlasov equlibria as solutions of a mixed Stjelties-Hilbert integral inverse problem. We apply these solutions to the steady state electron rich sheath associated with a non monotonic potential profile and an asymmetric potential minimum. The electron distribution on one side of this minimum is smooth, but differs from that on the other side, which is jump discontinuous on the separatrix, but otherwise stable against the bump on tail instability: their difference is related to the distribution of the finite mass, mobile ions, which is log singular at the virtual cathode.
2012, Articolo in rivista, ENG
NOCERA L; PALUMBO L J
We investigate the solutions of the kinetic Vlasov-Poisson equations, which govern a plasma made of electrons and one species of mobile ions, in one rectangular dimension. We present a new formulation of Poisson's equation as an integral inverse problem. We prove inversion formulas which allow us to write the solution of this problem in such a way that the energy distribution of either of the particle species is related, in a straightforward way, to the energy distribution of the other species. We show that these distributions are retrieved from the boundary values of suitable sectionally analytic functions. These latter functions are the extension of the particle distributions into their respective complex energy domains